There are different types of information design problems depending on whether there are multiple receivers or a single one, whether the system is dynamic or not, whether the receivers have private information or not, etc. The information design problems with a single receiver are referred to as “Bayesian persuasion” as first introduced in [1]}, where a geometric method of analyzing the information design problem is proposed.
Information design problems with more than one receiver are usually more complex since the solution must induce an equilibrium between the receivers. It is shown in [2]} that the set of outcomes in an information design problem with multiple receivers is indeed the set of Bayes-correlated equilibria, BCE, for the receivers. According to the definition of BCE in [2]}, the information shared with the receivers contains suggestions of what actions they should take. Therefore, an obedience condition has to be imposed on the strategy of the sender to make sure the receivers will follow the suggestions once they hear them. The obedience condition is the same as the conditions that are imposed in the definition of correlated equilibria.
